Definitely suck zinc lozenges (or allow them to dissolve in your mouth). The aftertaste isn't fun, but I toss in a bite of fruit or something after it's done dissolving and there's less problem with aftertaste. Now, the product recommends one every three or four hours, but I have better luck with 1/2 lozenge every two hours for a couple of days. I swear I get away with the pre-cold not developing into a full-blown cold most times if I do this.
However, if the cold is already mature, the zinc won't help. Forget trying zinc if that's the case; save your money and tastebuds and go to chicken soup or whatever you do. Studies show zinc lozenges reduce the length of the cold when you begin early, but my experience is that we can even avoid a full-blown cold by catching it very early.